SOLUTION: Solve the following system of equations by graphing. If the system is inconsistent or the equations are​ dependent, say so. 24x-4y=48 6x=y+12

Algebra ->  Graphs -> SOLUTION: Solve the following system of equations by graphing. If the system is inconsistent or the equations are​ dependent, say so. 24x-4y=48 6x=y+12      Log On


   

Question 1089059: Solve the following system of equations by graphing. If the system is inconsistent or the equations are​ dependent, say so.
24x-4y=48
6x=y+12
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
4y=24x-48, after rearranging, and that is y=6x-12
y=6x-12
These are dependent equations; they are the same line.
graph%28300%2C300%2C-10%2C10%2C-15%2C15%2C6x-12%29

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

24x-4y=48
6x=y%2B12
------------------------
24x-4y=48
6x-y=12
------------------------
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


24x-4y=48

6x-y=12





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


24x-4y=48 Start with the given equation



-4y=48-24x Subtract 24+x from both sides



-4y=-24x%2B48 Rearrange the equation



y=%28-24x%2B48%29%2F%28-4%29 Divide both sides by -4



y=%28-24%2F-4%29x%2B%2848%29%2F%28-4%29 Break up the fraction



y=6x-12 Reduce



Now lets graph y=6x-12 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+6x-12%29+ Graph of y=6x-12




So let's solve for y on the second equation


6x-y=12 Start with the given equation



-y=12-6x Subtract 6+x from both sides



-y=-6x%2B12 Rearrange the equation



y=%28-6x%2B12%29%2F%28-1%29 Divide both sides by -1



y=%28-6%2F-1%29x%2B%2812%29%2F%28-1%29 Break up the fraction



y=6x-12 Reduce





Now lets add the graph of y=6x-12 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+6x-12%2C6x-12%29+ Graph of y=6x-12(red) and y=6x-12(green)


From the graph, we can see that the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines. So there are an infinite number of solutions and the system is dependent.